Huge demand for good schools: Lining up for the lottery to win entrance to the Harlem Success Academy.Chad Rachman/New York Post

Huge demand for good schools: Lining up for the lottery to win entrance to the Harlem Success Academy. (Chad Rachman/New York Post)

A whopping one-third of the children enrolled in kindergarten in Harlem these days attend charter schools — an under-appreciated yet critical fact, and perhaps the hinge upon which the future of public-school choice in New York City swings.

And how are Harlem charter kids doing?

Fairly well, and not just the kindergarteners. That’s according to a new study by Stanford University researchers, who found that Harlem charter kids are outpacing their peers in traditional, or district, public schools.

No miracles have occurred; far from it. Both charter- and district-school performance in Harlem lags the city overall — and likely will for some time, given the neighborhood’s pervasive levels of poverty and social dysfunction.

But the study, done by Stanford’s Center for Research on Education Outcomes, is cause for real optimism. It found both charter and district schools to be registering gains in Harlem — but the charters are leading the way.

Overall, the researchers found that charter-school kids learn more in a year than do their district-school counterparts — especially in math.

This tracks city performance results, the most recent of which showed that eight of the 11 most successful elementary and middle schools in the five boroughs are charter schools — with four of those to be found in Harlem.

This isn’t just luck. Harlem was chosen nearly 20 years ago as ground zero for New York City’s charter-school movement, and for the most obvious of reasons: The need for alternatives to the then-pitiful status quo was obvious, and unequivocal success there would be a beacon for school choice bright enough to be seen everywhere.

“The advocates knew that locating one school here and one school there might make for a lot of individually successful schools,” said one present-at-the-creation powerhouse recently, “but they’d be diffused. There would be no large, single, unarguable example of success needed to make a case for more growth.”

The backers felt so strongly, he said, that “they said they’d walk away” absent a Harlem cluster.

Eva Moskowitz, the former city councilwoman who’s been a motive force behind city charters, agrees with the strategy. “I believe in market share,” she deadpanned yesterday.

Well, market share is what she got: More than 20 percent of the city’s 48,000 charter-school kids attend classes in Harlem, which now has 26 of New York’s 126 charter schools.

Much more to the point, Harlem charters have worked so well — none more so than Moskowitz’s own Harlem Success Academy schools — that thousands of parents compete in seating lotteries every year.

Most, sad to say, are bitterly disappointed.

But will they just suck it up?

Parents want what’s best for their kids. Once it becomes clear that there is an alternative, many — if not most — will seek it out.

Thus does the rolling snowball grow.

School-choice opponents anticipated this outcome early on, noted the fellow who’s been tracking the charter phenomenon since the outset.

“Randi [Weingarten, then president of the United Federation of Teachers] made it pretty clear that if the organizers stuck with the school-by-school approach, the opposition would be nominal. But [she] didn’t want to have to deal with a successful cluster.”

Yet an effort to create a cluster is precisely what she got, of course — and so the union’s opposition has been far from nominal. Indeed, it has been down-and-dirty and thumb-in-your-eye — and no wonder: The UFT sees the charter movement as an existential threat, and the Stanford report is further evidence that the union’s nightmare is slowly coming true.

Moskowitz, meanwhile, seems to be building on the cluster strategy to bring yet another potential ally into the fight: middle-class parents. She, and the movement, are branching out into the Upper West Side and Brownstone Brooklyn in an effort to bring charter choice into neighborhoods famous for translating public-school frustrations into direct, effective political action.

Give these parents a taste of charter-school success, and it’ll only be a matter of time before the union’s tools on the City Council and in Albany are singing a different tune.

Or so goes the theory.

In the real world, the odds are all but overwhelming that a UFT tool is going to be the next mayor of New York City — in which case the ground beneath the charter movement stands to shift substantially.

And not for the better.

Or so goes that theory.

But maybe Harlem parents have gotten used to having some public schools that actually put the best interests of their children first.